No lets co re e ow onsider som examples to illustra

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Unformatted text preview: es k know wheth it's rainin or not ra her ng aining? his u 296 In thi case, Ch is handler knows if it is ra aining or no (rain is pa of inform ot art mation set 1 and n rain is part of inform no p mation set 2 but he is sure wh 2) sn't hether Joey has his y umbr rella today (information set 1 is w where it's ra aining but he doesn't k know which node he is at in the informa e ation set, th he doesn't know if Joe has his umbrella hus f a or no ot). Defin nition: An extensive fo game is said to be a game of perfect rec if all pla orm s e f call ayers never r forge informatio once it is known an they nev forget th own prior moves. et on s nd ver heir For e example, th following game tree is not a ga he g e ame of perf fect recall... ...can you see w why? is onica does not know (i she can remembe if she's starting the i.e. n't er) e In thi case, Mo game or ending it (i.e. mak e g king a choic that lead to a term ce ds minal node... ...and payo offs). Essen ntially, she has forgott whether she has a ten r already turned left or turne right or, in fact, has not moved yet. ed s d ow omes very problematic in the gam theoretic c me c You can see ho this beco , t, want to consider game of perfec recall. es ct framework and, as a result we only w PER RFECT VS IMPERFEC INFORM CT MATION nition: Defin An extensive fo game is said to be a game of perfect info orm s e f ormation if all mation sets are single s etons (i.e. players can identify exa actly which node they inform are a when ma at aking a mov ve/decision) ). If the informatio sets are not all singletons, it is a game of imperfect information. e on 297 STRA ATEGIES Defin nition: A pure strategy for each player i {1,2,...,n} is a function i that associates ever ry inform mation set with one of the availab choices f ble s. Let's call the pu strategy sets i. Fo the follow s ure y or wing game (in extensive form) the pure strategy se for playe 1 and pla ets er ayer 2 are: 1 = {(L, 5), (L, 10), (R, 5), (R, 10)} 2 = {(u, a, b), (u, a, a), (u, b, b), (u, b...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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